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Uncertainty quantification for the family-wise error rate in multivariate copula models
Weierstrass Institute for Applied Analysis and Stochastics, Germany.
Humboldt-University, Germany.
Weierstrass Institute for Applied Analysis and Stochastics, Germany.
2015 (English)In: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 99, no 3, 281-310 p.Article in journal (Refereed) Published
Abstract [en]

We derive confidence regions for the realized family-wise error rate(FWER) of certain multiple tests which are empirically calibrated at a given (global)level of significance. To this end, we regard the FWER as a derived parameter of a multivariate parametric copula model. It turns out that the resulting confidence regions aretypically very much concentrated around the target FWER level, while generic multiple tests with fixed thresholds are in general not FWER-exhausting. Since FWERlevel exhaustion and optimization of power are equivalent for the classes of multipletest problems studied in this paper, the aforementioned findings militate strongly infavor of estimating the dependency structure (i.e., copula) and incorporating it in amultivariate multiple test procedure. We illustrate our theoretical results by considering two particular classes of multiple test problems of practical relevance in detail,namely multiple tests for components of a mean vector and multiple support tests.

Place, publisher, year, edition, pages
2015. Vol. 99, no 3, 281-310 p.
Keyword [en]
Delta method, Gumbel–Hougaard copula, Multiple testing, Simultaneous test procedure, Subset pivotality
National Category
Probability Theory and Statistics
Research subject
URN: urn:nbn:se:su:diva-127170DOI: 10.1007/s10182-014-0241-5OAI: diva2:907189
Available from: 2016-02-26 Created: 2016-02-26 Last updated: 2016-04-04Bibliographically approved

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Bodnar, Taras
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